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This article is cited in 16 scientific papers (total in 16 papers)
Recognizability of alternating groups by spectrum
I. B. Gorshkov
Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
Abstract:
The spectrum of a group is the set of its element orders. A finite group $G$ is said to be recognizable by spectrum if every finite group that has the same spectrum as $G$ is isomorphic to $G$. It is proved that simple alternating groups An are recognizable by spectrum, for $n\ne6,10$. This implies that every finite group whose spectrum coincides with that of a finite non-Abelian simple group has at most one non-Abelian composition factor.
Keywords:
finite group, simple group, alternating group, spectrum of group, recognizability by spectrum.
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Algebra and Logic, 2013, 52:1, 41–45
Bibliographic databases:
   
UDC:
512.542
Received: 18.07.2012
Revised: 04.12.2012
Citation:
I. B. Gorshkov, “Recognizability of alternating groups by spectrum”, Algebra Logika, 52:1 (2013), 57–63; Algebra and Logic, 52:1 (2013), 41–45
Citation in format AMSBIB
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Yu. V. Lytkin, “Groups critical with respect to the spectra of alternating and sporadic groups”, Siberian Math. J., 56:1 (2015), 101–106
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N. V. Maslova, “Finite simple groups that are not spectrum critical”, Proc. Steklov Inst. Math. (Suppl.), 292, suppl. 1 (2016), 211–215
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N. V. Maslova, “Finite groups with arithmetic restrictions on maximal subgroups”, Algebra and Logic, 54:1 (2015), 65–69
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M. A. Grechkoseeva, A. V. Vasil'ev, “On the structure of finite groups isospectral to finite simple groups”, J. Group Theory, 18:5 (2015), 741–759
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A. V. Vasil'ev, “On finite groups isospectral to simple classical groups”, J. Algebra, 423 (2015), 318–374
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A. M. Staroletov, “On recognition of alternating groups by prime graph”, Sib. elektron. matem. izv., 14 (2017), 994–1010
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Yu. V. Lytkin, “On finite groups isospectral to $U_3(3)$”, Siberian Math. J., 58:4 (2017), 633–643
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Yuri V. Lytkin, “On finite groups isospectral to the simple groups $S_4(q)$”, Sib. elektron. matem. izv., 15 (2018), 570–584
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M. A. Grechkoseeva, “On spectra of almost simple extensions of even-dimensional orthogonal groups”, Siberian Math. J., 59:4 (2018), 623–640
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Yuri V. Lytkin, “On finite groups isospectral to the simple group $S_4(3)$”, Sib. elektron. matem. izv., 16 (2019), 1561–1566
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Grechkoseeva M.A. Vasil'ev A.V. Zvezdina M.A., “Recognition of Symplectic and Orthogonal Groups of Small Dimensions By Spectrum”, J. Algebra. Appl., 18:12 (2019), 1950230
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Gorshkov I. Staroletov A., “on Groups Having the Prime Graph as Alternating and Symmetric Groups”, Commun. Algebr., 47:9 (2019), 3905–3914
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Yang N. Grechkoseeva M.A. Vasil'ev A.V., “on the Nilpotency of the Solvable Radical of a Finite Group Isospectral to a Simple Group”, J. Group Theory, 23:3 (2020), 447–470
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A. M. Staroletov, “O kompozitsionnykh faktorakh konechnykh grupp, izospektralnykh prostym klassicheskim gruppam”, Sib. matem. zhurn., 62:2 (2021), 422–440
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